Solve the right triangle? Round decimals to the nearest tenth?

Question

Image of the triangle There is a right triangle DEF with the adjacent is 12 and the acute angle of D being 25 degrees and E being the right angle... I have to figure out angle F, DF, and DE... I'm honestly not sure on what to do and i'm stressing out.. I may have worded this wrong or missed something but any help would be appreciated, thank you so much.

Answer 1

Angle $F$. Remember, the insides of a triangle add up to $180$ degrees.

Length of $DF$. Remember, $\sin \theta=\frac{opp}{hyp}=\frac{12}{DF}$

So we have $\sin 25=\frac{12}{DF}$. You can solve from here.

Length of $DE$. After you calculate angle $F$, then we know $\tan\theta=\frac{opp}{adj}=\frac{DE}{9}$

So we have $\tan \text{ (angle F)}=\frac{DE}{9}$. You can solve from here.